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JEE Main & Advanced Mathematics Differentiation Question Bank Derivative at a point Standard Differentiation

  • question_answer
    If \[y={{\log }_{\cos x}}\sin x\], then \[\frac{dy}{dx}\]is equal to

    A)            \[\frac{\cot x\log \cos x+\tan x\log \sin x}{{{(\log \cos x)}^{2}}}\]

    B)            \[\frac{\tan x\log \cos x+\cot x\log \sin x}{{{(\log \cos x)}^{2}}}\]

    C)            \[\frac{\cot x\log \cos x+\tan x\log \sin x}{{{(\log \sin x)}^{2}}}\]

    D)            None of these

    Correct Answer: A

    Solution :

               We have \[y={{\log }_{\cos x}}\sin x=\frac{\log \sin x}{\log \cos x}\]                    \[\therefore \frac{dy}{dx}=\frac{\cot x.\log \cos x+(\log \sin x)\tan x}{{{(\log \cos x)}^{2}}}\] .


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